Our style tends to be child led. Not full unschoolers, but the child has a lot of say about not so much what we do, but how we do it.
We used Miquon Math and somewhere in there switched to Singapore. When we got to multiplication, A. did not retain it. It didn't matter what I tried, it did not take. We did other math stuff that did not require multiplication, waiting for her brain to maybe wake up to multiplication. This went on for 3 years. One day I picked a used copy of multiplication songs at the Gathering Place. Within 2 weeks she knew the tables by heart.
It turns out her very visual mom was trying to teach her visually instead of by auditory means. It reinforced the learning styles that I was just becoming aware of (I didn't know I was a visual learner and that others didn't think in pictures until I was in my 30's. Once I found this out, it really helped communication with my auditory husband when we worked on home improvement projects. :o))
She went from a math hater to a math lover in about a year. To this day she arrives at math answers unconventionally. It works but it is not how it is explained in the books or how my husband and I were taught. I have learned to go with it. :o)
All of this happened when A. was 8-11ish and we were living in the countryside outside of Apex.
Update:
I talked with A. to verify dates. I think I am off about 1/2 a year to 1 year. We think she started multiplication when she was 7 and we still lived in Ohio. (We moved right after her 8th birthday and she remembers making the multiplication booklets with Miquon. We switched to Singapore a few months after moving here.)
By the time she started Math Olympiad, she was almost 11 and she knew the tables at that point. I remember I started her in Math Olympiad to give her another math viewpoint. She was not a math fan and had major reservations about the whole thing. :o) In her second year of Math Olympiad she placed in the top 10%
So I think it was more 10 - 10 1/2ish, not 11.
Lisa B in North Carolina
We use no formal schedule for learning.....our environment is resource rich with books, manipulatives, curriculum, games etc but we work from a completely child led perspective with adults and older teens facilitating what goes on.
My eldest learned in a traditional school, my second learned when she asked what multiplication meant... I used unifix cubes and showed her what 2 2's 3 2's etc looked like visually... she mastered the concept within a few moments and later taught herself double and triple digit multiplication in a way I have yet to understand completely! My 3rd child has special needs but memorized the multiplication tables from a School House Rock video we had... I discovered this when I found pages and pages of paper where she had written them all out...when asked she said she heard about it on the video and thought it was a neat idea.... my youngest who is now 8 seems drawn to numbers so he's constantly asking what this and that add up to and recently when asked by a grandparent what 2 times 12 was (he remarked there were ALOT of rolls in a package she pointed out it was 2 dozen) he quickly thought about it and said "oh that's 12 plus 12 which is 24" he's been doing that ever since with other numbers fascinated by the idea of grouping things together and counting them up.
Loren R in California
He was so ahead of other kids his age he was never coerced mathematically because the requirements were so below his ability. We are lucky to have a school where he is given freedom and support to pursue his interests.
When and how did your child(ren) learn multiplication tables? 1st/2nd grade, patterns, tricks, and deconstruction/breaking down problems in his head.
It was his own interest. He wanted to study more complex problems and realized that table recall would help. That is how we originally found your site, naturalmath.comhis recall is pretty good now for an incoming 3rd grader and he has been able to grasp more challenging and thus interesting problems. He likes algebra and I wish I knew more to keep him challenged. Unfortunately, he tends to make more progress in math during the summer than when his mind is full of school work of other subjects. It took a while, but one day, after weeks of on and off interest, he woke up finally understanding long division.... I guess he dreamed about a problem we had started the previous day that night.
Lena H in North Carolina
Study S......he still hasn't chosen any math, although he sometimes figures things out in his head when needed....he does well with concepts picked up on his own, uses a calculator for other things he needs (or other tools like
google)
nothing formal yet, he's 15 1/2
Still waiting, but not sure where he's headed so still letting him choose. Was planning to start some formal stuff this year.....just some basic stuff/ kinda review what he's picked up on his own....
Sue in California
Do you just want kids who already know their tables? R. has had almost no coercion in his math life, but he doesn't know many multiplication facts yet. I was just telling him what the "times tables" are, in the car yesterday. Even though there's really no coercion in his education, I think he likes to keep on the traditional schedule. He was upset often during this past year about not knowing how to read (even though he could read some). Now he reads, and is content about that, I think.
Knowing that kids often learn their 'multiplication facts' in third and fourth grade, I think he'll want to do that. I don't think it will be too hard for him. So I'd guess he'd be in your category 2. But there's no telling until it plays out.
Caroline in North Carolina
We are unschoolers, with brief forays into panic stricken "I hope I'm not screwing them up" modes. About a year and a half ago, I gave my then 7 year old daughter the book Addition the Fun Way, which she really enjoyed. She used to beg to do the flash cards. Thinking I had "found the key" i then coerced her to use the workbook that goes along with it, and pushed Times Tables the Fun way at her too. Initially, she liked Times Tables the fun way, but the workbooks frustrated her and her interest completely reversed itself. This all happened in a period of 2 months. We have done no math instruction since then. Initially she retained some of the facts, but those have left her now. She has recently developed her "own way" of figuring math out, and I'm really proud of her insightful learning.
We are still learning, but with absolutely no pressure.
Pat S
I have three grown unschooled kids - I have no idea if or when they came to "know" multiplication facts (have them memorized). I know they've gone to college and completed all the required college math with A grades - including calculus and statistics, so I would guess that they're pretty quick with multiplication by this time (ages 18, 22, and 25).
Your questions aren't going to elicit sensible answers from unschoolers. The premise, that at some time a person will memorize multiplication facts, is problematic.
Janice C in North Carolina
Two of my children were in school at the typical time multiplication tables are learned: so I won't include them. My youngest was pulled from school midway through second grade before times tables were introduced, and it is her that I will include here. One note for you to consider is that many unschoolers will not be able to answer your question because we don't really assess whether our kids have learned specific "subjects". We tend to be project oriented and not break things down into categories of knowledge.
As an unschooler, I don't check whether my child has learned her multiplication tables. She is 9 1/2 now and would be going into 4th grade if she were in school. I don't think she knows her multiplication tables. I don't plan to introduce the concept to her.
Michelle in California
"Waldorf Multiplication" by FaerieRebecca on Flickr
Now we do beanbag tossing games, chant and clap games and jump rope to each table. Just basic patty cake in rhythm going from the whole to the sum: ""two is two times one, four is two times two, six is three times two"" both hands clap straight out at the sum and then cross during problem.
0,1,2,5,10 and 11 came so easily through song and or nuemonic, so we really only focused on 3,4,6,7,8,9 and 12"
Rebecca S in California
Timez Attack drill game
We do use Right Start math curriculum as a spine/ follow-up.
He has learned most of them this past school year through a combination of Right Start math games and some time on the Times Attack computer game. He is 6 years old.
"capeaches45" in New York
Yes, my daughter has experienced little coercion in math.
When she was in the 1st grade with flash cards, also with computer games.
Linda K in Ohio
My dd will be 12 in December. She is very language oriented; words are her friends, numbers are not. She has a terrific memory when it comes to anything word oriented, but she is also very gifted in ballet. She can remember complex ballet combinations after listening/watching once or twice. All of her instructors are amazed by her memory with detail.
She has never had much interest in memorizing anything with numbers; however, this summer she is working on memorizing the multiplication tables-on her own initiative. We have always been very relaxed in our schooling, and I had pretty much written off long ago her memorizing the tables in a traditional fashion, but I didn't worry about it. Now, she has decided that, "it is time" for her to learn them. Much to her surprise, she has already learned much of the tables from exposure and use, in spite of herself.
I would guess that dd falls somewhere between category #2 and #3? BTW, I've never told her how much math/physics are involved in ballet. I'm waiting on her to figure it out!
Just to clarify, we have used some curricula when dd was interested, but we have never taken any formal tests.
Sandra B in North Carolina
Montessori multiplication beads
We have found that "math" needs to be done everyday. It has been hard finding curriculum that can keeps a child interested for more than 3-4 months. I love the way Montessori "teaches" math. It starts with concrete mathematical concepts. It would be great if an approach were available as a student gets to the higher level.
This is very interesting since both my kids followed the same pattern! I thought that by the end of 3 rd grad, they should know their multiplication tables. I remember my teacher in third grade, a very, very old and scary Catholic school teacher, call our name and we would have to get up and recite by memory a multiplication (2 or 3 or 4). So, with my first child I did everything to help him learn them. Hands-on activities, repetition, everything. Well, I gave up and gave him a break over the summer. When we restarted in September, voila, he new his tables without review! The same thing happened with my second son in the same way! My conclusion....like reading, learning the multiplication by memory is developmental and will only be truly learned when the brain is ready!
Mr. Steve in New Jersey
Good question. We used Miquon books and head games in the car (Guess my rule). Our oldest son now 12 also did use some "math" computer games of the reader rabbit series, but the others did not. Will ask my wife about the when question.
Update: None of the kids know their multiplication tables, not even the 12 year old. Which after some discussion I realized meant they do not know them "cold" so they can recite the facts quickly. Yet, we had my 12 year old take the Stanford Aptitude Test and he scored beyond 12th grade in the math areas. (I forget he exact term). So while being able to quickly recall math facts can be useful I was glad to see it did not affect his test scores (which I usually don't worry about, but at some point they will be used by others in college admissions). All that said I am not that worried about it, they can do mathematical reasoning which is what we generally focus on.
Kat S in Halifax, Canada
A YuGiOh meeting, by Lograi
I do not use any curricula. Where we live, there is quite a bit of flexibility in reporting to the local school board and no yearly testing.
I'd define my current educational style as unschooling. I should add that I never had any worry about my kid learning math skills. My attitude is that learning to read and learning in general is easy and enjoyable, and there's no set right time to learn any particular skill, with perhaps the exception of speaking a language fluently without an accent.
Our home is free of math anxiety. I love math, but I do not mind if my son loves math or not. He's free to pursue his own interests.
My son loved to play YuGiOh (a card game) from the age of 4 onward. As part of the game, he had to use subtraction to work out the 'life points' with large whole numbers. He also had to learn multiplication because each card had attack points (different for each card), and the attack could be multiplied by 'the number of monsters in the graveyard' (a number that also changed at any moment in the game).
He asked me how to do these things when he was 4. I explained several times and that was it. He made the logical step himself into smaller numbers with things like taking his birthday money to the store (at 4 yrs old) and figuring out on his own how many packs of YuGiOh cards he could buy with it.
He still does not have the multiplication table memorized (at age 13), but rather makes the calculation quickly by grouping and adding in his head.
As an aside, I realized much later that by playing YuGiOh he had absorbed easily the concept of place value. As another aside, my son has recently chosen to attend math lectures (that are designed for high achieving 15-17 yr olds) at a local university, and he enjoys them.
I want to point out that I really dislike games; card games, board games, computer games, etc. I also feel that it's a 'waste of money' to buy cards, etc. These are my personal biases that have no place influencing how my son chooses to allot his attention, and I respect his choices and support him in following where his interests lead him.
Multiplication Study Family Stories
Table of Contents
The main study page.
Brenda F in Ohio and North Carolina
We used Miquon Math and somewhere in there switched to Singapore. When we got to multiplication, A. did not retain it. It didn't matter what I tried, it did not take. We did other math stuff that did not require multiplication, waiting for her brain to maybe wake up to multiplication. This went on for 3 years. One day I picked a used copy of multiplication songs at the Gathering Place. Within 2 weeks she knew the tables by heart.
It turns out her very visual mom was trying to teach her visually instead of by auditory means. It reinforced the learning styles that I was just becoming aware of (I didn't know I was a visual learner and that others didn't think in pictures until I was in my 30's. Once I found this out, it really helped communication with my auditory husband when we worked on home improvement projects. :o))
She went from a math hater to a math lover in about a year. To this day she arrives at math answers unconventionally. It works but it is not how it is explained in the books or how my husband and I were taught. I have learned to go with it. :o)
All of this happened when A. was 8-11ish and we were living in the countryside outside of Apex.
Update:
I talked with A. to verify dates. I think I am off about 1/2 a year to 1 year. We think she started multiplication when she was 7 and we still lived in Ohio. (We moved right after her 8th birthday and she remembers making the multiplication booklets with Miquon. We switched to Singapore a few months after moving here.)
By the time she started Math Olympiad, she was almost 11 and she knew the tables at that point. I remember I started her in Math Olympiad to give her another math viewpoint. She was not a math fan and had major reservations about the whole thing. :o) In her second year of Math Olympiad she placed in the top 10%
So I think it was more 10 - 10 1/2ish, not 11.
Lisa B in North Carolina
My eldest learned in a traditional school, my second learned when she asked what multiplication meant... I used unifix cubes and showed her what 2 2's 3 2's etc looked like visually... she mastered the concept within a few moments and later taught herself double and triple digit multiplication in a way I have yet to understand completely! My 3rd child has special needs but memorized the multiplication tables from a School House Rock video we had... I discovered this when I found pages and pages of paper where she had written them all out...when asked she said she heard about it on the video and thought it was a neat idea.... my youngest who is now 8 seems drawn to numbers so he's constantly asking what this and that add up to and recently when asked by a grandparent what 2 times 12 was (he remarked there were ALOT of rolls in a package she pointed out it was 2 dozen) he quickly thought about it and said "oh that's 12 plus 12 which is 24" he's been doing that ever since with other numbers fascinated by the idea of grouping things together and counting them up.
Loren R in California
He was so ahead of other kids his age he was never coerced mathematically because the requirements were so below his ability. We are lucky to have a school where he is given freedom and support to pursue his interests.
When and how did your child(ren) learn multiplication tables? 1st/2nd grade, patterns, tricks, and deconstruction/breaking down problems in his head.
It was his own interest. He wanted to study more complex problems and realized that table recall would help. That is how we originally found your site, naturalmath.comhis recall is pretty good now for an incoming 3rd grader and he has been able to grasp more challenging and thus interesting problems. He likes algebra and I wish I knew more to keep him challenged. Unfortunately, he tends to make more progress in math during the summer than when his mind is full of school work of other subjects. It took a while, but one day, after weeks of on and off interest, he woke up finally understanding long division.... I guess he dreamed about a problem we had started the previous day that night.
Lena H in North Carolina
Study S......he still hasn't chosen any math, although he sometimes figures things out in his head when needed....he does well with concepts picked up on his own, uses a calculator for other things he needs (or other tools like
google)
nothing formal yet, he's 15 1/2
Still waiting, but not sure where he's headed so still letting him choose. Was planning to start some formal stuff this year.....just some basic stuff/ kinda review what he's picked up on his own....
Sue in California
Do you just want kids who already know their tables? R. has had almost no coercion in his math life, but he doesn't know many multiplication facts yet. I was just telling him what the "times tables" are, in the car yesterday. Even though there's really no coercion in his education, I think he likes to keep on the traditional schedule. He was upset often during this past year about not knowing how to read (even though he could read some). Now he reads, and is content about that, I think.
Knowing that kids often learn their 'multiplication facts' in third and fourth grade, I think he'll want to do that. I don't think it will be too hard for him. So I'd guess he'd be in your category 2. But there's no telling until it plays out.
Caroline in North Carolina
We are unschoolers, with brief forays into panic stricken "I hope I'm not screwing them up" modes. About a year and a half ago, I gave my then 7 year old daughter the book Addition the Fun Way, which she really enjoyed. She used to beg to do the flash cards. Thinking I had "found the key" i then coerced her to use the workbook that goes along with it, and pushed Times Tables the Fun way at her too. Initially, she liked Times Tables the fun way, but the workbooks frustrated her and her interest completely reversed itself. This all happened in a period of 2 months. We have done no math instruction since then. Initially she retained some of the facts, but those have left her now. She has recently developed her "own way" of figuring math out, and I'm really proud of her insightful learning.
We are still learning, but with absolutely no pressure.
Pat S
I have three grown unschooled kids - I have no idea if or when they came to "know" multiplication facts (have them memorized). I know they've gone to college and completed all the required college math with A grades - including calculus and statistics, so I would guess that they're pretty quick with multiplication by this time (ages 18, 22, and 25).
Your questions aren't going to elicit sensible answers from unschoolers. The premise, that at some time a person will memorize multiplication facts, is problematic.
Janice C in North Carolina
Two of my children were in school at the typical time multiplication tables are learned: so I won't include them. My youngest was pulled from school midway through second grade before times tables were introduced, and it is her that I will include here. One note for you to consider is that many unschoolers will not be able to answer your question because we don't really assess whether our kids have learned specific "subjects". We tend to be project oriented and not break things down into categories of knowledge.
As an unschooler, I don't check whether my child has learned her multiplication tables. She is 9 1/2 now and would be going into 4th grade if she were in school. I don't think she knows her multiplication tables. I don't plan to introduce the concept to her.
Michelle in California
We've made Waldorf style charts like this clock http://robinsunne.com/robinsunnes_multiplication_clock
We made a chart with crayon ironed on fabric that we fold and the girls use it while playing board games
We also made these wood boards
http://www.youtube.com/watch?v=lBbLhUbAopc
We've used gem manipulatives with story for all the processes and they've loved this! http://waldorfjourney.typepad.com/a_journey_through_waldorf/2008/07/the-four-proces.html
Now we do beanbag tossing games, chant and clap games and jump rope to each table. Just basic patty cake in rhythm going from the whole to the sum: ""two is two times one, four is two times two, six is three times two"" both hands clap straight out at the sum and then cross during problem.
0,1,2,5,10 and 11 came so easily through song and or nuemonic, so we really only focused on 3,4,6,7,8,9 and 12"
Rebecca S in California
He has learned most of them this past school year through a combination of Right Start math games and some time on the Times Attack computer game. He is 6 years old.
"capeaches45" in New York
Yes, my daughter has experienced little coercion in math.
When she was in the 1st grade with flash cards, also with computer games.
Linda K in Ohio
My dd will be 12 in December. She is very language oriented; words are her friends, numbers are not. She has a terrific memory when it comes to anything word oriented, but she is also very gifted in ballet. She can remember complex ballet combinations after listening/watching once or twice. All of her instructors are amazed by her memory with detail.
She has never had much interest in memorizing anything with numbers; however, this summer she is working on memorizing the multiplication tables-on her own initiative. We have always been very relaxed in our schooling, and I had pretty much written off long ago her memorizing the tables in a traditional fashion, but I didn't worry about it. Now, she has decided that, "it is time" for her to learn them. Much to her surprise, she has already learned much of the tables from exposure and use, in spite of herself.
I would guess that dd falls somewhere between category #2 and #3? BTW, I've never told her how much math/physics are involved in ballet. I'm waiting on her to figure it out!
Just to clarify, we have used some curricula when dd was interested, but we have never taken any formal tests.
Sandra B in North Carolina
This is very interesting since both my kids followed the same pattern! I thought that by the end of 3 rd grad, they should know their multiplication tables. I remember my teacher in third grade, a very, very old and scary Catholic school teacher, call our name and we would have to get up and recite by memory a multiplication (2 or 3 or 4). So, with my first child I did everything to help him learn them. Hands-on activities, repetition, everything. Well, I gave up and gave him a break over the summer. When we restarted in September, voila, he new his tables without review! The same thing happened with my second son in the same way! My conclusion....like reading, learning the multiplication by memory is developmental and will only be truly learned when the brain is ready!
Mr. Steve in New Jersey
Good question. We used Miquon books and head games in the car (Guess my rule). Our oldest son now 12 also did use some "math" computer games of the reader rabbit series, but the others did not. Will ask my wife about the when question.
Update: None of the kids know their multiplication tables, not even the 12 year old. Which after some discussion I realized meant they do not know them "cold" so they can recite the facts quickly. Yet, we had my 12 year old take the Stanford Aptitude Test and he scored beyond 12th grade in the math areas. (I forget he exact term). So while being able to quickly recall math facts can be useful I was glad to see it did not affect his test scores (which I usually don't worry about, but at some point they will be used by others in college admissions). All that said I am not that worried about it, they can do mathematical reasoning which is what we generally focus on.
Kat S in Halifax, Canada
I'd define my current educational style as unschooling. I should add that I never had any worry about my kid learning math skills. My attitude is that learning to read and learning in general is easy and enjoyable, and there's no set right time to learn any particular skill, with perhaps the exception of speaking a language fluently without an accent.
Our home is free of math anxiety. I love math, but I do not mind if my son loves math or not. He's free to pursue his own interests.
My son loved to play YuGiOh (a card game) from the age of 4 onward. As part of the game, he had to use subtraction to work out the 'life points' with large whole numbers. He also had to learn multiplication because each card had attack points (different for each card), and the attack could be multiplied by 'the number of monsters in the graveyard' (a number that also changed at any moment in the game).
He asked me how to do these things when he was 4. I explained several times and that was it. He made the logical step himself into smaller numbers with things like taking his birthday money to the store (at 4 yrs old) and figuring out on his own how many packs of YuGiOh cards he could buy with it.
He still does not have the multiplication table memorized (at age 13), but rather makes the calculation quickly by grouping and adding in his head.
As an aside, I realized much later that by playing YuGiOh he had absorbed easily the concept of place value. As another aside, my son has recently chosen to attend math lectures (that are designed for high achieving 15-17 yr olds) at a local university, and he enjoys them.
I want to point out that I really dislike games; card games, board games, computer games, etc. I also feel that it's a 'waste of money' to buy cards, etc. These are my personal biases that have no place influencing how my son chooses to allot his attention, and I respect his choices and support him in following where his interests lead him.